Iterative Computational Algorithm Research Articles

Численное моделирование водородопроницаемости с концентрационной зависимостью коэффициента диффузии

The paper presents a nonlinear mathematical model of alloys hydrogen permeability for membrane technologies of high-purity hydrogen production. Diffusion processes in the material bulk are taken into account as well as physical and chemical phenomena at the surface: adsorption, desorption and relatively fast dissolution. The iterative computational algorithm and software in Scilab have been developed to model the hydrogen permeability with dynamic boundary conditions and concentration-dependent diffusion coefficient.

Optimal feedback control law for automated vehicles in the presence of cyberattacks: A min–max approach

While automated vehicles (AVs) are expected to bring a wide range of benefits to future transportation systems, emerging AV technologies open a door for cyberattacks, where a select number of AVs are compromised to drive in an adversarial manner. This could result in network-wide increases in traffic congestion and energy consumption, degrading the performance of transportation systems. Hence, it is necessary to develop attack mitigation strategies for AVs as AVs gradually become a reality. However, this is rather challenging due to the lack of knowledge of adversaries. Limited prior studies have assumed attacks with a given probability distribution without considering their malicious intention, which is far from realistic due to the adversarial nature of potential attacks.In this study, we derive an optimal feedback control law for AVs in the presence of cyberattacks. Notably, attacks are only assumed to have a bounded magnitude without being subject to any specific statistical distribution, which is not only of theoretical interest but also relaxes the assumptions seen in prior studies. More importantly, to deal with lack of knowledge of malicious attacks, we, for the first time, formulate a min–max control problem to minimize the worst-case disturbance to traffic flow. Specifically, we present a mathematical framework for describing mixed-autonomy traffic involving AVs and human-driven vehicles (HVs), considering two typical types of attacks, namely false data injection attack on sensor measurements and malicious attack on AV control commands. Based on the framework presented, we derive a set of necessary conditions of optimality for the min–max control problem, based on which an iterative computational algorithm is developed for determining the optimal control (driving) strategy of AVs. The effectiveness of the proposed approach is demonstrated via extensive numerical simulations.

Protocol for iterative optimization of modified peptides bound to protein targets

Peptides are commonly used as therapeutic agents. However, they suffer from easy degradation and instability. Replacing natural by non-natural amino acids can avoid these problems, and potentially improve the affinity towards the target protein. Here, we present a computational pipeline to optimize peptides based on adding non-natural amino acids while improving their binding affinity. The workflow is an iterative computational evolution algorithm, inspired by the PARCE protocol, that performs single-point mutations on the peptide sequence using modules from the Rosetta framework. The modifications can be guided based on the structural properties or previous knowledge of the biological system. At each mutation step, the affinity to the protein is estimated by sampling the complex conformations and applying a consensus metric using various open protein-ligand scoring functions. The mutations are accepted based on the score differences, allowing for an iterative optimization of the initial peptide. The sampling/scoring scheme was benchmarked with a set of protein-peptide complexes where experimental affinity values have been reported. In addition, a basic application using a known protein-peptide complex is also provided. The structure- and dynamic-based approach allows users to optimize bound peptides, with the option to personalize the code for further applications. The protocol, called mPARCE, is available at: https://github.com/rochoa85/mPARCE/.

Optimal policy for integrating Autonomous Vehicles into the auto market

With the advent of emerging technologies, autonomous vehicles (AVs) are expected to become increasingly available to travelers. It is highly anticipated that there will be a transitional period when legacy vehicles (LVs) are gradually replaced by AVs before AVs take up a full penetration in the auto market. As a result, LVs and AVs will inevitably coexist during this period experiencing an interactive temporal evolution in terms of their market shares. Inspired by the classic Lotka–Volterra equations, we develop a continuous-time dynamical model capable of capturing such temporal evolution. A discrete choice model is constructed and incorporated into the dynamical model for describing the likelihood of choosing LVs or AVs. To achieve the desired temporal integration of AVs, monetary subsidies and investment in AV-specific transportation infrastructure are considered as decision variables to promote the adoption of AVs. Further, an optimal control problem is formulated with the objective of achieving a desired market penetration rate (MPR) of AVs at the end of the planning horizon, while minimizing the cost associated with AV subsidies and infrastructure investment. We prove the existence of an optimal AV integration policy. Moreover, we derive necessary conditions of optimality characterizing the mathematical properties of the optimal integration policy. Based on the optimality conditions derived, an iterative computational algorithm is developed to determine the time-dependent integration policy, which allows the government agency to appropriately subsidize AV purchases and invest in AV-specific infrastructure in an adaptive manner. Extensive numerical results are presented to show the effectiveness and robustness of the proposed approach under two distinct demand patterns. In addition, a systematic cost–benefit analysis is conducted, along with appropriate sensitivity analysis, to evaluate the desirability of the integration of AVs. Since the dynamical model is general and the decision variables are easy to implement, the procedures presented in this article will provide significant managerial insights for government agencies into developing long-term strategic planning policies.

Test and Theory for a Refined Structural Model of a Hirth Coupling

Abstract Hirth coupling transmits high torques in the rotating assemblies of compressors and turbines. Their mating surface contacts cause local changes in lateral shaft stiffness. This is affected by the teeth geometry, contact surface area, coupling preload, and surface finish at the contact faces. Industry practice ignores localized lateral flexibility from the Hirth coupling, or is guided by limited experience-based rules of thumb. The authors provide a novel modeling approach utilizing 3D solid finite elements which accounts for contact deformations, intricate interface teeth geometries, stress concentration, and surface finish. This provides an increased accuracy localized stiffness model for the Hirth coupling, to improve rotordynamic response predictions. Free–free natural frequencies of a test rotor including a Hirth coupling are experimentally measured. The rotor is instrumented with strain gauges for preload force measurements, and the Hirth coupling contacting surface profiles are measured with a stylus type surface profiler. A GW contact model is obtained from the measured surface profiles. An iterative computation algorithm is utilized to calculate Hirth coupling contact stiffness and contact pressure at the complex-shaped contact surfaces. Predicted and measured natural frequencies are compared versus preload.

DIFFERENCE SCHEME OF THE BOUNDARY VALUE PROBLEM OF CO2 TRANSPORT IN SANDY FOREST SOIL

In the context of anthropogenic environmental impact analysis, there is a need to study soil carbon dynamics. Since CO 2 transport and production depend on soil texture, air humidity, rainfall frequency, and other factors, mathematical description of the gaseous phase of soils in a specific area is a topical task. This work is based on a mathematical model of the production and transport of carbon dioxide in the circadian time range in forest soils typical of Eastern Fennoscandia. The model is focused on a comparative quantitative analysis of diffusive and convective components to assess the dynamics of soil respiration and changes in flow directions (towards the atmosphere and deep-lying horizons, to groundwater). In this paper, the transition to the dimensionless form of the model was implemented, an explicit–implicit difference scheme and an iterative computational algorithm for solving the boundary value problem of carbon dioxide transport in a soil horizon were proposed.

Three-Dimensional Solid Finite Element Contact Model for Rotordynamic Analysis: Experiment and Simulation

Abstract Conventional rotordynamic analyses generally treat the rotor as a continuous body without considering effect of clamped joints. However, in modern rotating machines, rotors are often assembled with multiple complex-shaped parts and joints, which may significantly affect rotordynamic behavior. Several authors have proposed methods for implementing contact effects in rotordynamic analysis, but a more general modeling method for handling arbitrary contact geometries with various levels of surface roughness is needed. The present paper suggests a new contact model for rotordynamic analysis of an assembled rotor-bearing system with multiple parts connected by multiple joints. A contact element formulation is presented using solid finite elements and statistics-based contact theories. A test arrangement was developed to validate the proposed contact model for varying interface surface roughness and preloads. An iterative computation algorithm is introduced to solve the implicit relation between contact stiffness and stress distribution. Prediction results, using the contact model, are compared with measured natural frequencies for multiple configurations of a test rotor assembly. A case study is performed for an overhung type rotor-bearing system to investigate the effect of contact interfaces, between an overhung impeller and a rotor shaft, on critical speeds.

Solving the Competitive Binding Equilibria between Many Ligands: Application to High-Throughput Screening and Affinity Optimization.

Modern small-molecule drug discovery relies on the selective targeting of biological macromolecules by low-molecular weight compounds. Therefore, the binding affinities of candidate drugs to their targets are key for pharmacological activity and clinical use. For drug discovery methods where multiple drug candidates can simultaneously bind to the same target, a competition is established, and the resulting equilibrium depends on the dissociation constants and concentration of all the species present. Such coupling between all equilibrium-governing parameters complicates analysis and development of improved mixture-based, high-throughput drug discovery techniques. In this work, we present an iterative computational algorithm to solve coupled equilibria between an arbitrary number of ligands and a biomolecular target that is efficient and robust. The algorithm does not require the estimation of initial values to rapidly converge to the solution of interest. We explored binding equilibria under ligand/receptor conditions used in mixture-based library screening by affinity selection-mass spectrometry (AS-MS). Our studies support a facile method for affinity-ranking hits. The ranking method involves varying the receptor-to-ligand concentration ratio in a pool of candidate ligands in two sequential AS-MS analyses. The ranking is based on the relative change in bound ligand concentration. The method proposed does not require a known reference ligand and produces a ranking that is insensitive to variations in the concentration of individual compounds, thereby enabling the use of unpurified compounds generated by mixture-based combinatorial synthesis techniques.

A parallel-in-time iterative algorithm for Volterra partial integro-differential problems with weakly singular kernel

Volterra partial integro-differential problems with weakly singular kernel attract a lot of attentions in recent years, thanks to the numerous real world applications. Solving this kind of PDEs in a parallel-in-time (PinT) pattern is difficult, because of the nonlocal property of time evolution. In this paper, we consider a class of representative problems and propose a novel iterative algorithm for PinT computation. In each iteration, we can solve the PDEs for all the discrete time points simultaneously via the diagonalization technique proposed recently. Convergence of the algorithm is analyzed by looking insight into the decreasing property of the convolution quadrature weights. We show that the convergence rate of the proposed algorithm is robust with respect to the discretization and problem parameters. Numerical results are reported to support our findings.

Practical Frank–Wolfe Method with Decision Diagrams for Computing Wardrop Equilibrium of Combinatorial Congestion Games

Computation of equilibria for congestion games has been an important research subject. In many realistic scenarios, each strategy of congestion games is given by a combination of elements that satisfies certain constraints; such games are called combinatorial congestion games. For example, given a road network with some toll roads, each strategy of routing games is a path (a combination of edges) whose total toll satisfies a certain budget constraint. Generally, given a ground set of n elements, the set of all such strategies, called the strategy set, can be large exponentially in n, and it often has complicated structures; these issues make equilibrium computation very hard. In this paper, we propose a practical algorithm for such hard equilibrium computation problems. We use data structures, called zero-suppressed binary decision diagrams (ZDDs), to compactly represent strategy sets, and we develop a Frank–Wolfe-style iterative equilibrium computation algorithm whose per-iteration complexity is linear in the size of the ZDD representation. We prove that an ϵ-approximate Wardrop equilibrium can be computed in O(poly(n)/ϵ) iterations, and we improve the result to O(poly(n) log ϵ−1) for some special cases. Experiments confirm the practical utility of our method.

Newton’s method: sufficient conditions for practical and input-to-state stability

Newton’s method is a classical iterative algorithm for the numerical computation of isolated roots of algebraic equations and stationary points of functions. While its application is ubiquitous in a plethora of fields, questions concerning its robust stability to uncertainties in problem data and numerical accuracy often arise in practice. This paper seeks to provide sufficient conditions for practical stability, input-to-state-stability (ISS), integral ISS (iISS) and incremental ISS (δISS) of Newton’s method in the presence of such uncertainties, and provide illustrative examples of their application.

Computation of Sum of Squares Polynomials from Data Points

We propose an iterative algorithm for the numerical computation of sums of squares of polynomials approximating given data at prescribed interpolation points. The method is based on the definition ...

Model of movement of the free boundary of hydride formation in a cylindrical shell of zirconium alloy

One of the most important requirements for the materials (zirconium alloys) used in the reactor active zone is low hydrogen absorptivity, since hydrogen-induced embrittlement may cause zirconium cladding damage. Depending on the hydrogen content and operation temperature, hydrogen may be present in zirconium alloys as a solid solution or as hydrides. Hydrides have the greatest embrittlement effect on alloys as they can initiate and enlarge cracks. The problem is to model the dynamics of the moving boundary of phase transition and to estimate the concentration distribution in the hydride and the solution. This paper presents a mathematical model of zirconium alloy hydrogenation taking into account the phase transition (hydride formation) and the iterative computational algorithm for solving the nonlinear boundary-value problem with free phase boundary based on implicit difference schemes. The study was carried out under state order to the Karelian Research Centre of the Russian Academy of Sciences (Institute of Applied Mathematical Research KarRC RAS).

Simulation of the Self-Organization Process of Carbon Nanotube Systems

In this paper, we develop a coarse grained numerical model for the simulation of a self-organization process for a system of carbon nanotubes under the applied electric field. The model describes the polarization of nanotubes in the system with an electric field and also includes the Van der Waals interaction between nanotubes. We develop an iterative computation algorithm for particle charges in the nanotube, providing a significant speedup of the computation. Another advantage of this algorithm is the better scaling of the computation time as a function of the system size. The results of the application of this model to computing the self-organization process of the dynamics of carbon nanotubes are demonstrated.

Possibilities of laser amplification and measurement of the field structure of ultrashort pulses in the range of 2.7 – 3μm in tellurite glass fibres doped with erbium ions

The amplification of ultrashort signals in the range 2.7 – 3 μm in active tellurite glass fibres with high Kerr nonlinearity and high concentration of erbium ions in the core is theoretically investigated under diode pumping at a wavelength of 0.975 μm. The possibility of producing pulses with the energy ∼10 nJ and the duration smaller than 100 fs with ∼20 dB gain is shown. Moreover, using a specially developed iterative computer algorithm, the possibility of determining the intensity and phase of the generated pulses by measuring their fundamental spectra and two additional spectra obtained by means of nonlinear-optical conversion in short pieces of these optical fibres is demonstrated. Optical fibre samples are made of high-purity TeO2 – ZnO – La2O3 – Na2O glasses with 1021 cm−3 concentration of erbium ions in the core and a low content of hydroxyl groups that causes small losses in the spectral range under consideration. The group velocity dispersions, effective mode fields, nonlinear coefficients and field overlap integrals of the LP01 fundamental modes with a doped core for optical fibres with different core diameters are calculated, and the emission and absorption cross sections are calculated basing on the experimental luminescence spectrum. The optimal parameters of the amplifier are determined by numerically modelling the dynamics of ultrashort pulses using the measured and calculated characteristics.

Numerical modelling of free boundary dynamics in ‘metal-hydride’ phase transition

One of the most important requirements for the reactor’s active zone materials (made of zirconium alloys) is low hydrogen absorptivity since hydrogen embrittlement may cause zirconium cladding damage. Depending on the hydrogen content and operation temperature, hydrogen may be present in zirconium alloys as a solid solution or as hydrides. Hydrides have the greatest embrittlement effect on alloys as they can form and enlarge cracks. The problem is to model the dynamics of the moving boundary of phase transition and to estimate the concentration distribution in hydride and in solution. This paper presents a mathematical model of zirconium alloy hydrogenation taking into account phase transition (hydride formation), and the iterative computational algorithm for solving the nonlinear boundary value problem with free phase boundary based on implicit difference schemes.

Wide consensus aggregation in the Wasserstein space. Application to location-scatter families

We introduce a general theory for a consensus-based combination of estimations of probability measures. Potential applications include parallelized or distributed sampling schemes as well as variations on aggregation from resampling techniques like boosting or bagging. Taking into account the possibility of very discrepant estimations, instead of a full consensus we consider a “wide consensus” procedure. The approach is based on the consideration of trimmed barycenters in the Wasserstein space of probability measures. We provide general existence and consistency results as well as suitable properties of these robustified Frechet means. In order to get quick applicability, we also include characterizations of barycenters of probabilities that belong to (non necessarily elliptical) location and scatter families. For these families, we provide an iterative algorithm for the effective computation of trimmed barycenters, based on a consistent algorithm for computing barycenters, guarantying applicability in a wide setting of statistical problems.

Learning Subject-Specific Directed Acyclic Graphs With Mixed Effects Structural Equation Models From Observational Data.

The identification of causal relationships between random variables from large-scale observational data using directed acyclic graphs (DAG) is highly challenging. We propose a new mixed-effects structural equation model (mSEM) framework to estimate subject-specific DAGs, where we represent joint distribution of random variables in the DAG as a set of structural causal equations with mixed effects. The directed edges between nodes depend on observed exogenous covariates on each of the individual and unobserved latent variables. The strength of the connection is decomposed into a fixed-effect term representing the average causal effect given the covariates and a random effect term representing the latent causal effect due to unobserved pathways. The advantage of such decomposition is to capture essential asymmetric structural information and heterogeneity between DAGs in order to allow for the identification of causal structure with observational data. In addition, by pooling information across subject-specific DAGs, we can identify causal structure with a high probability and estimate subject-specific networks with a high precision. We propose a penalized likelihood-based approach to handle multi-dimensionality of the DAG model. We propose a fast, iterative computational algorithm, DAG-MM, to estimate parameters in mSEM and achieve desirable sparsity by hard-thresholding the edges. We theoretically prove the identifiability of mSEM. Using simulations and an application to protein signaling data, we show substantially improved performances when compared to existing methods and consistent results with a network estimated from interventional data. Lastly, we identify gray matter atrophy networks in regions of brain from patients with Huntington's disease and corroborate our findings using white matter connectivity data collected from an independent study.

Retrial multi-server queuing system with PHF service time distribution as a model of a channel with unreliable transmission of information

• A multi-server retrial queueing system with unreliable service is analyzed. • The ergodicity condition is derived. • New effective algorithm for computing the stationary distribution of level-dependent AQTMC is developed. • Performance measures of the system are computed. • Numerical results showing advantages of the proposed algorithm are presented. A multi-server retrial queue with a Markovian arrival process , as well as possible customer non-persistency and unreliable operation of servers, is analysed. The service of a customer (transmission of information) consists of a random number of phases. During a transmission, a failure can occur. The failure does not cause server breakdown or its subsequent recovery. The failure occurrence during service of a customer implies either that the departure of the customer from the server (the customer joins an orbit and retries later), the customer re-starts complete service immediately, or the customer resumes the service from the phase at which the failure occurred. The total occupation time of a server by a customer has a so-called PHF (phase-type with failures) distribution. The dynamics of the system are described by a multi-dimensional level-dependent Markov chain . An infinitesimal generator of the chain is derived. To obtain the ergodicity condition, we prove that the Markov chain belongs to the class of asymptotically quasi-Toeplitz Markov chains. Because we consider a multi-server queuing system, the dimensions of the blocks of the generator can be large. Thus, the use of a standard algorithm to find a stationary distribution of an asymptotically quasi-Toeplitz Markov chain can face problems in the stage of computer implementation. We develop a new efficient iterative algorithm for approximate computation of the stationary distribution that computes many times faster and requires much fewer computer resources than the standard algorithm. The advantages of the new algorithm and some features of the model under consideration are numerically demonstrated.

Numerical modelling of dynamics of free boundary of hydride formation

One of the most important requirements for the reactor's active zone materials (made of zirconium alloys) is low hydrogen absorptivity since hydrogen embrittlement may cause zirconium cladding damage. Depending on the hydrogen content and operation temperature, hydrogen may be present in zirconium alloys as a solid solution or as hydrides. Hydrides have the greatest embrittlement effect on alloys as they can form and enlarge cracks. The problem is to model the dynamics of the moving boundary of phase transition and to estimate the concentration distribution in hydride and in solution. This paper presents a mathematical model of zirconium alloy hydrogenation taking into account phase transition (hydride formation), the iterative computational algorithm for solving the nonlinear boundary-value problem with free phase boundary based on implicit difference schemes, and the results of computational experiments.